In [1]} Uchino introduced a notion of generalized Rota-Baxter operator as an operator analogue of Poisson structures in the noncommutative setup. Later, generalized Rota-Baxter operators are also named as relative Rota-Baxter operators or \(\mathcal {O}\) -operators [2]}, [3]}. They are mostly known as relative Rota-Baxter operators in the literature. Let \(A\)  be an associative algebra and \(M\)  be an \(A\) -bimodule. A linear map \(R : M \rightarrow A\)  is said to be a relative Rota-Baxter operator if
\(R(m) \cdot R(m^{\prime }) = R (R(m) \cdot _M m^{\prime } ~+ ~ m \cdot _M R(m^{\prime })),~\text{ for } m, m^{\prime } \in M.\) 
